A train travelling at a speed of 75 mph enters a tunnel 3½ miles long. The train is ¼ mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?

Given Data

• Speed of train = 75 miles per hour (mph)
• Length of tunnel = 3½ miles = 3.5 miles
• Length of train = ¼ mile = 0.25 mile

Step 1: Determine total distance to be covered
To clear the tunnel, the front of the train must travel the tunnel length and the rear must also clear the tunnel by the train length. Total distance = Tunnel length + Train length = 3.5 + 0.25 = 3.75 miles

Step 2: Use Time = Distance ÷ Speed
Time (in hours) = 3.75 ÷ 75 = 0.05 hour

Step 3: Convert hours to minutes
0.05 hour × 60 = 3 minutes

Final Answer
The train takes 3 minutes to pass completely through the tunnel.